Fibonacci Sequence–Based Design and Analysis of Stable Second-Order LTI Systems

Fibonacci sequence, known for its mathematical elegance & recurrence properties, brings a novel approach to filter design. In this paper we aim to design 2nd order linear time invariant (LTI) systems using pairs of consecutive higher order Fibonacci numbers. The analyses of designed systems for their overall stability i.e in terms of Routh-Hauritz criterion, gain and phase margins reveal that all the designed transfer function are stable. The impulse response represents Dirac delta function and the step response is slightly over damped with damping ratio ζ ≈ 1.029. The magnitude response is similar to that of a low pass filter. Monte Carlo Simulations to predict their cut off frequency validates the theoretical analysis. We have showed that the cut off frequency is 0.618 times the square root of the product of Fibonacci pairs.